SOLUTION: log(x+3)=1-logx

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Question 75293: log(x+3)=1-logx
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%2B3%29%29=1-log%28x%29
log%28%28x%2B3%29%29+%2B+log%28x%29+=+1
log%28%28x%2A%28x%2B3%29%29%29+=+1
log%28%28x%5E2+%2B3x%29%29+=+1
Note that log%2810%29+=+1, so
x%5E2+%2B+3x+=+10
x%5E2+%2B+3x+-+10+=+0
%28x+%2B+5%29%28x+-+2%29+=+0
x = -5
x = +2
check
log%28%28x%2B3%29%29=1-log%28x%29
log%28%28-5%2B3%29%29=1-log%28%28-5%29%29
x = -5 cannot be a solution, because no exponent with a positive base
can give a negative result
Try x = +2
log%28%282%2B3%29%29=1-log%282%29
log%285%29=1-log%282%29
log%285%29+%2B+log%282%29+=+1
log%28%285%2A2%29%29+=+1
log%2810%29+=+1
1+=+1
OK x = +2 is the answer